Energy absorption capability of nanocomposites: A

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Composites Science and Technology 69 (2009) 2392–2409

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Review

Energy absorption capability of nanocomposites: A review Lingyu Sun a, Ronald F. Gibson b,*, Faramarz Gordaninejad b, Jonghwan Suhr b a b

School of Transportation Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China Department of Mechanical Engineering, University of Nevada, Reno, Nevada 89557, USA

a r t i c l e

i n f o

Article history: Received 20 March 2009 Received in revised form 23 June 2009 Accepted 24 June 2009 Available online 30 June 2009 Keywords: A. Nanocomposites B. Impact behavior B. Interface B. Fracture toughness C. Crack

a b s t r a c t Experimental evidence shows that some nanocomposites with special matrices and filler materials may achieve significant and simultaneous improvements in stiffness, fracture toughness, impact energy absorption and vibration damping, and these characteristics could be of particular importance in automobile or airplane structures. This paper reviews relevant literature which deals with various manifestations of energy absorption of composites from the nano to the macro-scale, with emphasis on the nano-scale. Energy absorption mechanisms in nanocomposites will be examined, along with important influence factors, such as shape, dimension and stiffness of particles, type of matrix, particle volume fraction, distribution of particles and the particle–matrix interfacial properties by both experiments and simulation methods. Relevant potential applications will be discussed, and the key related issues that need to be resolved in the future will be addressed. Ó 2009 Elsevier Ltd. All rights reserved.

Contents 1. 2. 3.

4. 5.

6. 7.

Introduction and overview of energy absorption in composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental characterization of energy absorption in composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental evidence of improved energy absorption due to nano-reinforcements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Effects of particle stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Effects of particle geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Effects of inter-particle distance and volume fraction of fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Effects of particle size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5. Effects of stochastic variation of particle size and strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Effects of type of polymer matrix and fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7. Effects of interfacial adhesion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8. Distribution status of fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9. Nano-reinforcement of conventional composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10. Summary of experimental evidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation of energy absorption in nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy absorption mechanisms in nano-reinforced composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Comparison of energy from pull-out/debonding and fracture of fillers in micro- and nano-scale reinforced polymers . . . . . . . . . . . . . 5.2. Formation of interphases between matrix and nano-fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Factors influencing the interfacial properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1. Shape and aspect-ratio of fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2. Particle size-based critical debonding stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3. Surface morphology and pretreatment of nano-fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4. Type of filler and matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.5. Interfacial slip and damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6. Dispersion status and toughness mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Other toughness mechanisms in nano-reinforced composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of nano-reinforcements for energy absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and recommendations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

* Corresponding author. Tel.: +1 775 784 1489; fax: +1 775 784 1701. E-mail address: [email protected] (R.F. Gibson). 0266-3538/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2009.06.020

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1. Introduction and overview of energy absorption in composites Energy absorption is an increasingly important function of structural materials for several reasons. For example, structural crashworthiness is now an essential requirement in the design of automobiles, rail cars, aircraft and rotorcraft. The crashworthy structure is designed such that in the event of a crash, it absorbs the impact energy in a controlled manner before the energy gets transmitted into the passenger compartment. Traditionally, metals have been the most commonly used materials for crashworthy structural applications, mainly due to their plastic deformation characteristics that enable them to absorb impact energy in a controlled manner [1]. Unlike metals, polymer composite materials do not typically exhibit plastic deformation, although their stress– strain relationships may show signs of other types of nonlinearities, but they are superior to metals for specific energy absorption. Polymer-based nanocomposites offer the potential for simultaneous improvement of several properties, including toughness [2]. Other manifestations of energy absorption in structural materials are internal damping, which is important for the control of vibrations and fatigue, and fracture toughness, which is a measure of the energy required for crack growth and fracture. When the dimensions of the reinforcement fibers or particles approach the nanometer scale, a number of effects cause the properties of the corresponding composites to be different from those of composites reinforced with macro-scale particles. The main factors affecting the properties of nanocomposites include nano-filler dispersion, dimensions, volume fraction, the nature of the matrix material, the interfacial characteristics between nano-filler and matrix, and the manufacturing process [3]. At present, most of the research results on energy absorption in composites have relied on experiments and by varying design parameters, such as the type of filler, size or volume fraction [4,5]. However, it is not easy to intuitively predict the energy absorption properties of the resulting nanocomposites due to the anisotropic properties and morphology of the nano-particles. Thus, it is desirable to carry out analytical or numerical analyses to understand how particles affect the mechanical behavior of the composite. Various approaches including molecular dynamics simulations, continuum mechanics, elastic shell theory, and finite element analysis have been investigated. However, due to theoretical limitations, the aforementioned modeling methods have their own shortcomings [6]. Multi-scale analyses have been conducted for nanoparticle-reinforced polymeric composites by incorporating molecular mechanical models into continuum models in recent years [6]. Although numerous new nanocomposites have been developed in various research fields, the research on energy absorption capability of nanocomposites is still in the early stages. There are several technical issues to be addressed: (1) lack of acceptable evaluation parameters and methods for energy absorption capability of nanocomposites, such as evaluating indicators, test methods and test conditions; (2) lack of theoretical models that can predict the energy absorption capability; (3) lack of a systematic comparison of limitations and advantages among the existing research methods; (4) lack of a fundamental understanding of energy absorption mechanisms in nanocomposites; (5) need for finding potential applications of energy-absorbing nanocomposites. The purpose of this work is to review relevant literature related to energy absorption of composites having constituent dimensions ranging from the nano-scale to the macro-scale, with emphasis on the nano-scale. Energy absorption mechanisms in nanocomposites as well as key design factors, effective experiments and simulation methods will be reviewed. Moreover, potential applications will be

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discussed, and the key technical issues that need to be solved in the future will be also addressed. While review articles and even books on energy absorption in conventional composites have been published [7–11], the authors concluded that a review article on energy absorption in nanocomposites has not yet been published, and that such an article should be of significant value to the composites research community. 2. Experimental characterization of energy absorption in composites In the following, two key concepts will be discussed: (1) structural energy absorption capability and, (2) material properties which are related to the material energy absorption capability. Two common tests [7] are often used for examining the energyabsorbing capabilities of composite structures: the axial crush [1] and bending crush [12] tests of thin-walled structural components. Axial crush tests can be carried out under either quasi-static loading or impact loading. The static axial collapse tests can be performed between the parallel steel plates of a hydraulic press at very low crosshead speed, such as 1 mm/min, while the corresponding dynamic tests can be conducted by a direct impact using a drop hammer or an impactor. Due to its simplicity, many researchers have used the quasi-static test [1]. Although the cross section of the samples may have various geometries [13–17], most experiments on polymer composites have been carried out using axisymmetric cylindrical tubes, mainly because they are easy to fabricate. Typical dimensions of composite tubes are 50–100 mm length, 50 mm internal diameter and 2–3 mm wall thickness. Limited results are also available on flat plates [18], sine webs [14], cones [15], square and hexagonal tubes [16]. The typical crushing deformation modes of composite tubes in axial compression are shown in Ref. [19]. Similar tests in bending can be performed using three- or four-point loading of composite tubes or shells. The energy absorbed by the collapsed specimen during the axial crushing process is calculated by measuring the non-recoverable area (not including the recoverable elastic strain energy) under the corresponding load, P, versus shell shortening (displacement) s curve. The total area under the curve, including both recoverable and non-recoverable areas, is given by



Z

Pds

ð1Þ

and the non-recoverable area is Wp = W  We, where We is the elastic strain energy. The energy absorption capability of an axially loaded shell of a given material is typically quantified by the specific energy absorption (SEA), specific absorbed energy (SAE) or special energy (Es). This is defined as the ratio of the energy absorbed, Wp, for the collapsed specimen, to the crushed mass, mc, which is calculated as the crushed volume, vc, times the material density q.

SEA ¼

Wp Wp ¼ mc qv c

ð2Þ

The SEA has been widely used to evaluate the energy absorption capability of structures [20–24]. Assuming that such tubes could be manufactured using nanocomposites, their SEA values could be obtained from crush testing to evaluate energy absorption capability. However, no publications on crushing of nanocomposite tubes have been found, and this appears to be an area in need of exploration. Other related material properties, such as the impact strength [3,25], notched Charpy or Izod impact toughness [2], fracture toughness [26–28], strain energy release rate [29], fracture en-

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ergy [30], essential work of fracture [31–33], non-recoverable area under the stress–strain curve [34,35], and loss modulus [36] or loss factor [37,38] during vibration are useful indicators of material energy absorption capability, and are the focus of this paper. Among the above properties, the fracture toughness for the mode I crack is most often studied. Energy release rate, another measure of fracture toughness, is the energy dissipated during fracture per unit of newly created fracture surface area. These two parameters can be obtained from double cantilever beam (DCB) tests, single edge notched bending (SENB) tests [39], or compact tension (CT) tests [40]. Toughness or impact toughness is defined as the amount of energy per volume that a material can absorb before rupturing. Impact strength is the impact stress necessary to fracture a material. The impact toughness and strength can be obtained from Izod impact test. 3. Experimental evidence of improved energy absorption due to nano-reinforcements It has been recently reported that the energy absorption capability and related properties of composite materials can be engineered by adding micro or nano-scale fillers. For example, micron-sized rigid or elastic particles such as glassy spheres or rubber particles, or rigid nano-sized particles such as SiO2, TiO2, CaSiO3, Al2O3 powder, carbon nanotubes (CNTs) and clay nanoplatelets have been used, and some important findings are summarized in this section. 3.1. Effects of particle stiffness Increasing the amount of micro soft/elastic fillers improves the impact toughness, but reduces the modulus of elasticity of a polymer blend [2]. On the other hand, increasing the amount of micro hard/rigid fillers improves both the impact toughness and the modulus of elasticity of such materials [2,5]. For example, the addition of rigid CaCO3 with 600 nm diameter (0.2 vol.%) in high density polyethylene (HDPE), the impact strength improves more than 200% [41]; the addition of Al2O3 nano-particles into epoxy resin simultaneously improves stiffness, impact energy and failure strain at low filler contents (1–2 vol.%) [42]. Such improvements are not typically observed for composites reinforced with conventional micro-particles. Core shell rubber (CSR) nano-particles having a soft rubber core and a glassy shell were found to improve the fracture toughness of an epoxy vinyl ester resin significantly more than MMT nano-clay particles having the same weight fraction, but hybrid blends of CSR and nano-clay were found to yield the best balance of toughness, modulus and strength [43]. The same investigators reported that when the nano-clay particles were used to enhance the polymer matrix material in a conventional glass fiber-reinforced composite, the interlaminar fracture toughness of the composite was less than that of the composite without the nano-clay particles [44]. Alignment of the nano-clay particles along the fiber axis was suggested as a possible reason for this result. The capacity of rigid particles for energy dissipation at high loading rates depends on two factors [45]: (i) the ability of the dispersed particles to detach from the matrix and to initiate the matrix local shear yielding in the vicinity of the voids and (ii) the size of the voids. So, the optimal minimal rigid particle size for polymer toughening should satisfy two main requirements: (i) to be smaller than the critical size for polymer fracture and (ii) to have a debonding stress which is small compared to the polymer matrix yield stress. Elastomers are also able to increase their energy-absorbing capacity by both acting as stress concentration sites and affecting properties (type and content of crystalline phase) of the matrix [46,47].

3.2. Effects of particle geometry Particles, tubes and platelets are three kinds of typical reinforcement. Silica or aluminum oxide particles, nano-fibers or nanotubes and nano-clay platelets are the most widely studied materials. The impact toughness of polymers containing inorganic nanofillers such as MMT (Montmorillonite) based polymer composites was found to decrease [2], while adding Al2O3 nano-whiskers, glass fibers and wollastonite in a polymer resin improved the fracture toughness, KIC, compared with that of the unreinforced resin [48]. Significant improvement of impact strength of polymeric nanocomposites was achieved by adding amino-functionalized MWCNTs [49] or small amounts of SWCNTs [50]. The impact toughness of PMMA (polymethyl-methacrylate) has been improved considerably by the addition of CNTs [50], and the toughness and modulus of MWCNTs reinforced PP exhibited a maximum at 1 wt.% CNTs [51,52]. In addition, the impact toughness and stiffness of nanotube–reinforced polymer composites have been found to be functions of the Young’s modulus of the nanotubes [53]. 3.3. Effects of inter-particle distance and volume fraction of fillers Viana [2] reports that, based on Wu’s experimental observation [54], toughening of particle modified semi-crystalline polymers is related to the inter-particle distance s, independently of the type of added particles (Fig. 1). The distance s relates both to the concentration, u, and the average size d of the particles. Fig. 2 [55] shows a significant improvement in toughness when the inter-particle distance s becomes smaller than the particle diameter, d. Similarly, Wetzel et al. [56] observed an experimental increase of the fracture toughness with increasing particle-diameter-to-spacing distance ratio, and compared it with theoretical data presented in Ref. [57]. Qi et al. [58] observed that the fracture toughness and modulus of DGEBA epoxy resin increased with increasing volume fraction of nano-clay particles. 3.4. Effects of particle size To study different toughening or energy absorption effectivenesses for fillers with micro- or nano-scale size, d, Ng et al. [59] measured tensile properties of TiO2 (32 nm)/epoxy nanocomposites and compared them with those of composites having micron-size TiO2 (0.24 lm). It was shown that the nanocomposite has a higher failure strain than the microcomposite. Javni et al. [60] found that micro- and nano-silica fillers, although of the same chemical origin, had considerably different effects on mechanical properties of rigid and flexible polyurethane foams. The compression strength of flexible polyurethane foams with nano-silica fillers was increased, while the rebound resilience decreased. However,

Fig. 1. Geometric parameters in nanoparticle-reinforced composites.

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Fig. 2. Correlations between inter-particle distance and toughness for SiO2/epoxy nanocomposite [55].

the addition of micro-fillers in flexible foams lowered hardness and compression strength, but increased rebound resilience, indicating a higher energy dissipation in nano-silica-filled foams. Cho et al. [61] varied the size of reinforcing particles from the macro (0.5 mm) to the nano (15 nm) scale and found that the interfacial fracture toughness does not depend on particle size, but increases substantially when the sliding fracture mode occurs. The effects of particle size on stress–strain curves for spherical alumina particle-reinforced vinyl ester composites are shown in Fig. 3 [61], where it is seen that the Young’s modulus increases slightly with reductions in particle size for both micron-scale and nano-scale particles. Fig. 3 also shows that, while the tensile strength increases with reductions in particle size for micron-scale particles, the tensile strength decreased with reduced particle size for nano-scale particles. Poor dispersion of the nano-particles was suggested as the reason for the latter result. Chen et al. [62] found analytically that there is a peak of damage dissipation (the energy dissipation due to damage evolution) at the critical particle radius, r0cr. From Fig. 4 [62] one can see that if d < 2r0cr, where d/2 is the average particle radius, the energy dissipation increases monotonically with increasing d in the nanometer range. However, the energy dissipation decreases monotonically with increasing d when d > 2r0cr. Maharsia et al. [63,64] used 40 lm (R40) and 75 lm (R75) size rubber particles (2 vol.%) and nano-clay Nanomer I. 30E with 2 vol.% (C2) and 5 vol.% (C5) to modify the four different

Fig. 3. Effect of particle size on stress–strain curves for 3 vol.% alumina particles with various diameters d in vinyl ester resin [61].

Fig. 4. Energy dissipation due to interfacial debonding in polymeric matrix against average radius of reinforcing particles from nanometer size to micrometer size for different initial volume fractions, fpo [62].

density matrix microstructures in syntactic foams, M22, M32, M38, M46, respectively. From the total area under flexural load–displacement curves [63], the energy absorption increased upon the addition of rubber particles, and the amount of energy absorbed is higher in foams containing the smaller 40 lm particles. The lower flexural strength of nano-clay foams due to the clusters of nanoclay may have caused lower energy absorption in these foams. However, another study [65] found that both short micro-fibers and nano-clay Nanomer I.30TC caused a substantial increase in toughness in polymer syntactic foam. The micro-fiber toughening was more effective than nano-toughening in this case, except for nano-clay-reinforced syntactic foam containing 1 wt.% nano-clay which showed equal or better fracture properties compared with short fiber-reinforced syntactic foam. Adding micro-sized particles in a nanocomposite (e.g., CaSiO3 micro-particles in a 2 vol.% Al2O3 nanoparticle-reinforced epoxy nanocomposite increased the flexural modulus [42], but the Charpy impact energy was negatively affected. Wetzel et al. [42] also compared the bending energy absorption of composites made from alumina (Al2O3) particles of 40 nm, 1 lm and 3 lm in diameter in a vinyl ester resin, and found that the flexural modulus was not affected by the particle size, but the strength was lowered as the particle size decreased. The decrease in strength with reduced particle size was attributed to poor dispersion of nano-particles in the composite. To find the effects of volume fraction and dispersion of fillers and the area under the stress–strain curve, Gupta [66] incorporated 2% and 5% surface modified nano-clay particles into three types of syntactic foams with different densities and studied the compressive properties. It was found that the toughness of the material, as determined by the area under the stress–strain curve, increased by 80–200% for various nano-enhanced foams tested in the study. Ye et al. [67] found that the impact strength of epoxy increases by 4 by adding merely 2.3 wt.% HNTs (natural nanotubes from halloysite, a clay mineral with the chemical formula Al2Si2O5(OH)4). The toughness effect due to high specific surface area (SSA) can be demonstrated by adding nano-fillers such as CNTS and carbon black in the neat polymer. The fracture toughness of nano-reinforced composites is typically increased compared with that of the neat polymer if agglomeration is minimized [68].

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3.5. Effects of stochastic variation of particle size and strength The stochastic variation in the strength of individual CNTs, may have a direct effect on the fracture mechanisms as in micro-based fiber composites. Barber et al. [69] measured the Weibull shape and scale parameters of the tensile strength distribution of MWCNTs grown by chemical vapor deposition (CVD), and found wide variability of strength. The importance of these two parameters is summarized by Barber et al. [70]. Tomar et al. [71] found that a microstructure less prone to fracture shows higher variations in fracture response when compared to the one which offers least resistance to crack propagation. In addition, for a particular micro-structural morphology, the levels of variations in the crack surface area generated and the variations in the energy release rate are of the same order as the levels of variations in constituent properties. 3.6. Effects of type of polymer matrix and fillers An example here is that the reinforcement of PP and PE with 4 wt.% nano-clay leads to a striking variation in impact toughness behavior under identical processing conditions. The impact strength of the PP nanocomposite increases, while that of the PE nanocomposite decreases due to the stronger PP–clay interaction and the weak PE–clay interaction [72], as explained by a load sharing mechanism [73]. There is a strong correlation between the fracture toughness and the percolation network of the particle agglomeration [74]. Perhaps a denser network of clustered particles exists in the PP matrix. The tightly bonded and uniformly distributed particles exist between the nano-particles and the polymer matrix, which may lead to a more ductile and tougher polymeric matrix in the inter-particle regions, and this may also enhance the fracture toughness. The majority of semi-crystalline polymers such as PE and PP are ductile at low strain rates, but at high strain rates experienced in the Izod impact test, they are characterized by a brittle behavior [72]. When replacing Laponite clay with equivalent amounts of MMT clay in polymer–clay nanocomposites gradually, the loss moduli in the multilayered films increase [75]. 3.7. Effects of interfacial adhesion Direct experimental probing of interfacial adhesion in single CNT/polymer system has been carried out [76]. Using AFM (atomic force microscopy), Barber [77,78] measured the force required to separate a CNT from a solid polymer matrix by performing reproducible nanopullout experiments and calculated the fracture energy for the nanotube–polymer interface from the measured pull-out forces and embedded lengths. Podsiadlo et al. [79] studied the reinforcement mechanism of PVA/MMT (polyvinyl alcohol/montmorillonite) obtained from the LBL (layer-by-layer) process and found that the structural organization of clay platelets maximizes the number of polymer/MMT interactions and constraints the polymer-chain motion, which results in a highly efficient load transfer between the polymer phase and the stiff MMT platelets. Windle [80] suggested two questions on how to compare conventional composites with nanocomposties. One is how to analyze the energy absorbed per unit cross sectional area by fiber pull-out, the other is how to determine the effect of specific surface area for nano or macro particles? The van der Waals forces in a CNT/polymer or polymer-chain in PVA/MMT interact strongly with two or three fillers, which increases the interfacial strength and the energy required to form cracks. Miyagawa et al. [40] found that inferior adhesion at the interface is preferred for impact energy absorption, but it is difficult to improve the Izod impact strength for a rigid epoxy material

by adding organo-clay nano-platelets. The fracture toughness and critical energy release rate was found to be correlated with the fracture surface roughness of nano-clay/epoxy [40] and silica platelet/epoxy [30], and it is assumed that a rough fracture surface is an indication of good adhesion between the particles and the matrix. 3.8. Distribution status of fillers Some experiments have shown that fracture toughness improved with addition of clay nano-platelets to epoxy when the clay nano-platelets were not fully exfoliated, and intercalated clay nano-platelets were present [40]. Miyagawa et al. [40] measured the lengths of exfoliated clay nano-platelets in the range of 70– 380 nm, while those of intercalated clay nano-platelets were 600–800 nm, because the thickness of clay nano-platelet is only 1 nm and the nano-platelets are easily broken during the manufacture of exfoliated clay. Similarly, the fracture toughness of intercalated clay nano-platelet-reinforced biobased epoxy was found to be improved more than the fracture toughness of the corresponding exfoliated nano-platelet-reinforced composite [81]. 3.9. Nano-reinforcement of conventional composites Since the longitudinal compressive failure of conventional continuous fiber-reinforced composites typically occurs at a stress level that is 40–50% below the tensile strength of the composites [82], improving the toughness under longitudinal compression loads is important. Uddin and Sun [83] showed that when a silica nanoparticle-enhanced epoxy (Nanopox) was used as the matrix material in a unidirectional E-glass fiber-reinforced composite, both the longitudinal compressive modulus and strength of the composite were significantly improved. In related work, the same authors found that the interlaminar fracture toughness and impact resistance properties of the same nanoparticle-enhanced composite were improved by comparison with the composite without nano-particles [84]. Miyagawa et al. [85] observed that the addition of 5 wt.% of intercalated clay nano-platelets to the biobased epoxy matrix in a carbon/epoxy composite resulted in significant improvement of the critical energy release rate, but only slight improvement resulted from the addition of exfoliated clay nanoplatelets. The interlaminar fracture toughness of carbon-fiber-reinforced epoxy/nano-clay nanocomposites (CFRENCs) was increased by 85% with the introduction of 4 parts of nano-clay per hundred of epoxy by mass in the epoxy matrix [86]. The experiments of Yokozeki et al. [87] showed that the addition of cup-stacked carbon nanotubes (CSCNT) significantly improved both Mode I and Mode II interlaminar fracture toughness of conventional carbon-fiber-reinforced epoxy laminates. CSCNTs were added at the ply interfaces by either sprinkling between the prepreg layers during layup or placement of CSCNT-dispersed resin films between the layers during layup. Improvement of interlaminar fracture toughness in the CSCNT-enhanced composites was attributed to crack deflection and creation of rougher fracture surfaces. However, experiments by Gibson et al. [88] yielded no improvement in Mode I interlaminar fracture toughnesses of unidirectional carbon/epoxy laminates when MWNTs were sprinkled at ply interfaces during the layup process. It was suggested that, although the MWNTs were initially well-dispersed before sprinkling, they reclustered during the curing process, and this may have caused the delamination crack to jump through the clusters as it propagated. Addition of 10 wt.% of organosilicate nano-clay to the epoxy matrix of a conventional fiber-reinforced composite was found to increase the fracture toughness [89]. Addition of a very low volume fraction of silica nano-particles to an epoxy mold-

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ing compound filled with micro-silica particles resulted in the improvement of fracture toughness by a factor of two, and the crack deflection and plastic deformation of a matrix material induced by the silica nano-particles are shown schematically in Fig. 5 [39]. 3.10. Summary of experimental evidence Table 1 lists the energy absorption variation due to the addition of various nano-particles in polymer matrix materials. Table 2 compares the effects of micro and nano-filler materials. Major conclusions that may be drawn from these tables are as follows: (1) by adding both nano-scale and micro-scale particles, it is possible to reduce impact strength or failure strain or impact energy; (2) unmodified MMT has a negative effect on impact or fracture toughness; (3) modification/surface treatment of fillers, such as organMMT (montmorillonite treated with an organic surfactant agent) or modified nano-CaCO3 is very effective in improving impact energy; (4) using only a small amount of nano-particles can be as effective as using large micro-particles in increasing fracture toughness; (5) micro-fibers are more effective than nano-clay in increasing fracture toughness and critical strain energy release rate in polymer syntactic foam; (6) nano-silica particles in polyurethane (PU) foam matrix increases damping whereas micro-silica particles do not [60]; (7) CNTs, organ-clay, nano-TiO2, nano-CaCO3, nano-Al2O3, and nano-silica particles all are good inclusions for improving the energy absorption capability of nanocomposites, if dispersed uniformly. 4. Simulation of energy absorption in nanocomposites Although experimental methods [106,108] are convenient for comparing the effects of type and volume fraction of filler on the energy absorption capabilities of composite materials, it is difficult to experimentally determine how each constituent in the composite influences the energy absorption, and the interaction mechanisms between filler and matrix may be more important for energy absorption in nanocomposites than they are is for conventional composites [109]. The large difference that exists in lengthscale between nano-fillers and macro-samples of nanocomposites for energy absorption tests make it difficult to develop acceptable structure-property models for simulating energy absorption. Analytical or numerical methods for simulating various aspects of energy absorption in nanocomposites include molecular dynamics (MD) simulation [110,111], continuum mechanics [112–114], elastic shell theory [24,115], finite element methods (FEM) [116– 124] and multi-scale modeling methods [125–131,115] which connect the data from the nano scale to the macro-scale. MD simulation considers an individual single-walled carbon nanotube (SWCNT) as an assembly of large numbers of atoms, which are connected through atomic forces (Fig. 6a) and has been used for the study of nano-scale fracture and crack propagation of

Fig. 5. Schematic diagram of crack propagation and toughening mechanism of silica particle-filled epoxy molding compound (SN-EMC) nanocomposites [39].

Table 1 Summary of the energy absorption effectiveness of nanocomposite materials containing different fillers. Type of filler

Matrix

Effect

Refs.

Nano-particles Al2O3 (5, 10 vol.%) Aluminum Silica particle Silica particle Powder SiO2 Colloidal SiO2 SiO2 (5 wt.%) SiO2 (3, 7 wt.%) SiO2 (10 wt.%) TiO2 (1, 3 vol.%) TiO2 (2 vol.%) TiO2 (300 nm)

Epoxy PMMA Epoxy Epoxy PP PP Araldite-F Epoxy Epoxy PA66 HIPS Epoxy

FT " (60%, 120%) IE " 80% (10 layers) FT " GIC " DA " FT " GIC " FS " IS " 21% IS " 68% FT " 72% GIC " 141% FT " FT " (7 wt.%) FT " 122% GIC 288% EWF " (69%, 183%) IS " > 20% FT "

[56] [25] [84] [89] [90] [90] [91] [92] [93] [33] [3] [56]

Nanotubes CNTs DWCNTs CNTs (3 vol.%) MWCNT (1 vol.%) MWCNT (1/3/5 vol.%) MWCNTs (1 wt.%) MWCNTs (1 wt.%) HNTs (2.3 wt.%) Carbon fiber

PMMA Epoxy Al2O3 PP HDPE Rubbery epoxy Glassy epoxy Epoxy Epoxy/CNTs

IT " FT " FT " 79% IS " FE " (T > Tt) EWF " IS " 29%FS " 30% IS " 50%FS " 60% IS " (400%) FT "

[2] [94,95] [96] [97] [4] [98] [98] [67] [99]

Nano-clay MMT Organ-MMT (4 wt.%) Clay (4 wt.%) Clay (4 wt.%) MMT Carbon fiber Clay Clay Nano-EPR Clay (0.5 wt.%) Organ-clay (0.5 wt.%) Nano-clay (2.5 vol.%) Nano-clay (2.5 vol.%) MMT

Polymeric PA6 PP Polyethylene Epoxy Epoxy/clay POE/PP EPR/PA6 PA6 Epoxy Epoxy LD-Foam MD-Foam Fiber/epoxy

IT ; EWF " IS " FT " IS " IS ; FT ; IFS " 85% IS ; IS ; IS " IS " 72% IS " 137% TA " (80%, 125%) TA " (150%, 200%) IE "

[2] [31] [72] [72] [28] [86] [32] [46] [46] [100] [100] [66] [66] [101]

PP, polypropyrene; PA, polyamide; PMMA, poly(methyl-methacrylate); HIPS, highimpact polystyrene; HDPE, high density polyethylene; POE, polyethylene octane; EPR, elastomer particle; EWF, essential work of fracture; DA, damage area; FT, fracture toughness; IFT, interlaminar fracture toughness; IE, impact energy; FE, fracture energy; IT, impact toughness; IS, impact strength; FS, failure strain; LD, low density; MD, medium density; TA, total area under r–e curve; GIC, mode I strain energy release rate; IFS, impact fracture strength.

CNTs [132,133]. The simulation results have shown that the Stone– Wales defect is a typical mechanism for fracture of CNTs under tension [133], and can be used to estimate fracture strains and stresses of CNTs [133]. Lordi and Yao [134] used MD to study the binding energies and sliding frictional stresses between pristine CNTs and a range of polymer substrates, and found that they play only a minor role in determining the strength of the interface. Frankland [135] used MD to analyze the influence of chemical cross-links in SWFNTs/polymer composites on the shear strength, and calculated the critical length required for load transfer. Liao [136] found that interface adhesion between CNTs and polystyrene come from the electrostatic forces, van der Waal’s interaction and the mismatch in coefficient of thermal expansion, as well as the radial deformation induced by atomic interactions. Although MD can provide accurate local results, the accuracy is highly dependent on the initial boundary conditions [137], the computation time is long and the investment in facilities is huge for simulation of large systems of atoms [138]. Lau [139] developed an analytical approach based on elastic shell theory to study the interfacial bonding characteristics of nanotube/polymer composites. Continuum mechanics based FEM can be used to calculate the fracture properties of macro composite samples very quickly

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Table 2 Comparison between energy absorption characteristics of micro and nano-scale filler materials. Fillers

Matrix

Effect

Refs.

Nano-CaCO3 (15 wt.%/6 vol.%) Nano-CaCO3 (15 wt.%/6 vol.%) Nano-CaCO3 (5, 10 wt.%) Micro CaCO3 (30 vol.%) Micro CaCO3 (0.7 lm) Nano-particle (a < 140 nm) micro-particle (a > 140 nm) Micro CaSiO3 (